Finite Group Databasebeta

← #13075545

Subgroups — #13075545

Order 1408.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C212yesmaximal
2C11×#389C211yesmaximal, characteristic, complemented
3#10622606C212yesmaximal, complemented
4#10622602C212yesmaximal, complemented
5#10622597C212yesmaximal, complemented
6#10622552C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic, complemented
8#10622287C212yesmaximal, complemented
9#10622281C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26#66947—28no—
27C11×#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C23×D11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×D44—41no—
42C2×D44—41no—
43C2×D44D414yes—
44C2×C4×D11—24no—
45C2×C4×D11—42no—
46C2×C4×D11—42no—
47C11×C4⋊C4—24no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—41no—
50C42×C11—41no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56C4⋊Dic11—22no—
57C4⋊Dic11—41no—
58C4⋊Dic11—41no—
59Dic11⋊C4—24no—
60Dic11⋊C4—42no—
61#2724—111nomaximal, Sylow
62C23×C11C2411yescharacteristic
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11C2×D414yes—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11C2×D412yes—
83C2×C4×C11#4112yes—
84C2×C4×C11#4112yes—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94D44—44no—
95C4×D11—48no—
96C2×#123—112no—
97#398—112no—
98#397—112no—
99#397—112no—
100#390—111no—
101#389—111no—
102#389D1111yescharacteristic, complemented
103#385—112no—
104#385—112no—
105C22×C11C22×D411yescharacteristic
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4111yescharacteristic
108C22×C11H(5,𝔽2)11yescharacteristic
109C22×C11H(5,𝔽2)11yescharacteristic
110C22×C112−1+411yescharacteristic
111C22×C112−1+411yescharacteristic
112C2×D11—24no—
113C2×D11—24no—
114C2×D11—24no—
115C2×D11—42no—
116C2×D11—42no—
117C2×D11—42no—
118C2×D11—42no—
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—22no—
122C4×C11—42no—
123C4×C11—42no—
124Dic11—42no—
125Dic11—42no—
126Dic11—42no—
127C22×D4—111no—
128C23×C4—112no—
129#123—228no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—111no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4C2×D1112yes—
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4—112no—
142C2×C22⋊C4—112no—
143C2×C42C2×D1111yescharacteristic
144#95—112no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95C2×D1112yes—
149C2×C11#53411yescharacteristic
150C2×C11#53911yescharacteristic
151C2×C11#53911yescharacteristic
152C2×C11#54711yescharacteristic
153C2×C11#54711yescharacteristic
154C2×C11#55911yescharacteristic
155C2×C11#56311yescharacteristic
156D11—44no—
157C24—112no—
158C2×D4—114no—
159C2×D4—441no—
160C2×D4—441no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4—224no—
165C22×C4—442no—
166C22×C4—442no—
167C22×C4C22×D1112yes—
168C22×C4C22×D1112yes—
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1111yescharacteristic
171C22×C4C22×D1111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—24no—
174C4⋊C4—41no—
175C4⋊C4—224no—
176C4⋊C4—222no—
177C4⋊C4—442no—
178C4⋊C4—441no—
179C4⋊C4—441no—
180C22⋊C4—224no—
181C22⋊C4—224no—
182C22⋊C4—224no—
183C22⋊C4—224no—
184C22⋊C4—224no—
185C42—41no—
186C11#272411yescharacteristic, complemented, Sylow
187C23—114no—
188C23—222no—
189C23—222no—
190C23—222no—
191C23—222no—
192C23—222no—
193C23—222no—
194C23C23×D1111yescharacteristic
195D4—444no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—448no—
218C2×C4#433912yes—
219C2×C4D4×D1112yes—
220C2×C4#434312yes—
221C22—224no—
222C22—224no—
223C22—224no—
224C22—442no—
225C22—442no—
226C22—442no—
227C22—442no—
228C22C2×#433911yescharacteristic
229C22C2×D4×D1111yescharacteristic
230C22#6703711yescharacteristic
231C22C2×#434311yescharacteristic
232C22#6704011yescharacteristic
233C22#6704211yescharacteristic
234C22#6704311yescharacteristic
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—442no—
241C4—442no—
242C4—442no—
243C2—444no—
244C2#1062304611yescharacteristic
245C2#1062308211yescharacteristic
246C2#1062311611yescharacteristic
247C2#1062313611yescharacteristic
248C2#1062317611yescharacteristic
249C2#1062323011yescharacteristic
250C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC22×D44C22
hypercenter#389D11
hypocenterC11#2724
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#389C2semidirect
3. #10622606C2semidirect
4. #10622602C2semidirect
5. #10622597C2semidirect
7. #10622541C2semidirect
8. #10622287C2semidirect
9. #10622281C2semidirect
102. #389D11semidirect
186. C11#2724semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#669472
C11×#3892
#106226062
#106226022
#106225972
#106225522
#106225412
#106222872
#106222812
#272411